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<div class="title">W:/Products/Vtl/branches/v1.0/Vtl/Vtl/include/Vtl/impl/intersections.hpp</div>  </div>
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<a href="intersections_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="preprocessor">#include &quot;<a class="code" href="geometry_8h.html">Vtl/geometry.h</a>&quot;</span>
<a name="l00002"></a>00002 <span class="preprocessor">#include &lt;Eigen/StdVector&gt;</span>
<a name="l00003"></a>00003 <span class="preprocessor">#include &lt;utility&gt;</span>
<a name="l00004"></a>00004 <span class="preprocessor">#include &lt;map&gt;</span>
<a name="l00005"></a>00005 
<a name="l00006"></a>00006 <span class="keyword">namespace </span>Vtl
<a name="l00007"></a>00007 {
<a name="l00008"></a><a class="code" href="namespace_vtl_1_1intersections.html">00008</a>         <span class="keyword">namespace </span>intersections
<a name="l00009"></a>00009         {
<a name="l00010"></a>00010                 <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar, <span class="keywordtype">int</span> Dimension&gt;
<a name="l00011"></a><a class="code" href="namespace_vtl_1_1intersections.html#a98449060e8a8660d4a37a3623dfe8271">00011</a>                 <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespace_vtl_1_1intersections.html#a98449060e8a8660d4a37a3623dfe8271" title="Intersects two lines(Rays).">lineWithLineIntersection</a>(<span class="keyword">const</span> Eigen::ParametrizedLine&lt;Scalar, Dimension&gt; &amp;_LineA,
<a name="l00012"></a>00012                         <span class="keyword">const</span> Eigen::ParametrizedLine&lt;Scalar, Dimension&gt; &amp;_LineB, 
<a name="l00013"></a>00013                         Eigen::Matrix&lt;Scalar, Dimension, 1&gt; *_Point <span class="comment">/*= NULL*/</span>,
<a name="l00014"></a>00014                         <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;_Eps <span class="comment">/*= 1e-4*/</span>)
<a name="l00015"></a>00015                 {
<a name="l00016"></a>00016                         <span class="keyword">typedef</span> Eigen::Matrix&lt;Scalar, Dimension, 1&gt; VectorType;
<a name="l00017"></a>00017                         <span class="keyword">typedef</span> Eigen::ParametrizedLine&lt;Scalar,Dimension&gt; ParametrizedLine;
<a name="l00018"></a>00018 
<a name="l00019"></a>00019                         ParametrizedLine seg = <a class="code" href="namespace_vtl_1_1intersections.html#abcfbdb5e7051cb57a8b79d4dd821d129" title="Returns the shortest line segment between two lines(Rays).">lineToLineSegment</a>(_LineA, _LineB, _Eps);                 
<a name="l00020"></a>00020                         <span class="keywordtype">double</span> sqr_dist = seg.direction().squaredNorm();
<a name="l00021"></a>00021                         <span class="keywordflow">if</span>(sqr_dist&lt;_Eps)
<a name="l00022"></a>00022                         {
<a name="l00023"></a>00023                                 <span class="keywordflow">if</span>(_Point!=NULL)
<a name="l00024"></a>00024                                         *_Point = seg.origin();
<a name="l00025"></a>00025                                 <span class="keywordflow">return</span> (<span class="keyword">true</span>);
<a name="l00026"></a>00026                         }
<a name="l00027"></a>00027                         <span class="keywordflow">return</span> (<span class="keyword">false</span>);
<a name="l00028"></a>00028                 }
<a name="l00029"></a>00029 
<a name="l00030"></a>00030                 <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar, <span class="keywordtype">int</span> Dimension&gt;
<a name="l00031"></a><a class="code" href="namespace_vtl_1_1intersections.html#abcfbdb5e7051cb57a8b79d4dd821d129">00031</a>                 <span class="keyword">inline</span> Eigen::ParametrizedLine&lt;Scalar, Dimension&gt; <a class="code" href="namespace_vtl_1_1intersections.html#abcfbdb5e7051cb57a8b79d4dd821d129" title="Returns the shortest line segment between two lines(Rays).">lineToLineSegment</a>(<span class="keyword">const</span> Eigen::ParametrizedLine&lt;Scalar, Dimension&gt; &amp;_LineA,
<a name="l00032"></a>00032                         <span class="keyword">const</span> Eigen::ParametrizedLine&lt;Scalar, Dimension&gt; &amp;_LineB,
<a name="l00033"></a>00033                         <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;_Eps <span class="comment">/*= 1e-4*/</span>)
<a name="l00034"></a>00034                 {
<a name="l00035"></a>00035                         <span class="keyword">typedef</span> Eigen::Matrix&lt;Scalar, Dimension, 1&gt; VectorType;
<a name="l00036"></a>00036                         <span class="keyword">typedef</span> Eigen::ParametrizedLine&lt;Scalar,Dimension&gt; ParametrizedLine;
<a name="l00037"></a>00037 
<a name="l00038"></a>00038                         <span class="comment">// point + direction = 2nd point</span>
<a name="l00039"></a>00039                         VectorType p1 = _LineA.origin();
<a name="l00040"></a>00040                         VectorType dir1 = _LineA.direction();
<a name="l00041"></a>00041                         VectorType p2 = p1 + dir1;
<a name="l00042"></a>00042 
<a name="l00043"></a>00043                         <span class="comment">// point + direction = 2nd point</span>
<a name="l00044"></a>00044                         VectorType q1 = _LineB.origin();
<a name="l00045"></a>00045                         VectorType dir2 = _LineB.direction();
<a name="l00046"></a>00046                         VectorType q2 = q1 + dir2;
<a name="l00047"></a>00047 
<a name="l00048"></a>00048                         <span class="comment">// a = x2 - x1 = line_a[1] - line_a[0]</span>
<a name="l00049"></a>00049                         VectorType u = dir1;
<a name="l00050"></a>00050                         <span class="comment">// b = x4 - x3 = line_b[1] - line_b[0]</span>
<a name="l00051"></a>00051                         VectorType v = dir2;
<a name="l00052"></a>00052                         <span class="comment">// c = x2 - x3 = line_a[1] - line_b[0]</span>
<a name="l00053"></a>00053                         VectorType w = p2 - q1;
<a name="l00054"></a>00054 
<a name="l00055"></a>00055                         <span class="keywordtype">double</span> a = u.dot (u);
<a name="l00056"></a>00056                         <span class="keywordtype">double</span> b = u.dot (v);
<a name="l00057"></a>00057                         <span class="keywordtype">double</span> c = v.dot (v);
<a name="l00058"></a>00058                         <span class="keywordtype">double</span> d = u.dot (w);
<a name="l00059"></a>00059                         <span class="keywordtype">double</span> e = v.dot (w);
<a name="l00060"></a>00060                         <span class="keywordtype">double</span> denominator = a*c - b*b;
<a name="l00061"></a>00061                         <span class="keywordtype">double</span> sc, tc;
<a name="l00062"></a>00062                         <span class="comment">// Compute the line parameters of the two closest points</span>
<a name="l00063"></a>00063                         <span class="keywordflow">if</span> (denominator &lt; _Eps)          <span class="comment">// The lines are almost parallel</span>
<a name="l00064"></a>00064                         {
<a name="l00065"></a>00065                                 sc = 0.0;
<a name="l00066"></a>00066                                 tc = (b &gt; c ? d / b : e / c);  <span class="comment">// Use the largest denominator</span>
<a name="l00067"></a>00067                         }
<a name="l00068"></a>00068                         <span class="keywordflow">else</span>
<a name="l00069"></a>00069                         {
<a name="l00070"></a>00070                                 sc = (b*e - c*d) / denominator;
<a name="l00071"></a>00071                                 tc = (a*e - b*d) / denominator;
<a name="l00072"></a>00072                         }
<a name="l00073"></a>00073                         <span class="comment">// Get the closest points</span>
<a name="l00074"></a>00074 
<a name="l00075"></a>00075                         VectorType pt1 = p2 + sc * u;
<a name="l00076"></a>00076                         VectorType pt2 = q1 + tc * v;
<a name="l00077"></a>00077                         <span class="keywordflow">return</span> ParametrizedLine(pt1, (pt2 - pt1));
<a name="l00078"></a>00078                 }
<a name="l00079"></a>00079 
<a name="l00080"></a>00080                 <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar, <span class="keywordtype">int</span> Dimension&gt;
<a name="l00081"></a><a class="code" href="namespace_vtl_1_1intersections.html#a05704aa101f3c820534f3d8f7eda7243">00081</a>                 <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespace_vtl_1_1intersections.html#a05704aa101f3c820534f3d8f7eda7243" title="Intersects a line with a polygon face.">lineWithFaceIntersection</a>(<span class="keyword">const</span> Eigen::ParametrizedLine&lt;Scalar, Dimension&gt; &amp;_Line,
<a name="l00082"></a>00082                         <span class="keyword">const</span> <a class="code" href="class_vtl_1_1_polygon.html">Polygon&lt;Scalar, Dimension&gt;</a> &amp;_Face,
<a name="l00083"></a>00083                         Eigen::Matrix&lt;Scalar, Dimension, 1&gt; *_Point <span class="comment">/*= NULL*/</span>,
<a name="l00084"></a>00084                         <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;_Eps <span class="comment">/*= 1e-4*/</span>)
<a name="l00085"></a>00085                 {
<a name="l00086"></a>00086                         <span class="keyword">typedef</span> Eigen::Matrix&lt;Scalar, Dimension, 1&gt; VectorType;
<a name="l00087"></a>00087                         <span class="keyword">typedef</span> Eigen::Hyperplane&lt;Scalar, Dimension&gt; Hyperplane;
<a name="l00088"></a>00088 
<a name="l00089"></a>00089                         <span class="keywordflow">if</span>(_Face.size()&lt;3)
<a name="l00090"></a>00090                                 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00091"></a>00091 
<a name="l00092"></a>00092                         VectorType u = _Face[1] - _Face[0];
<a name="l00093"></a>00093                         VectorType v = _Face[2] - _Face[1];
<a name="l00094"></a>00094                         VectorType normal = u.cross(v).normalized();
<a name="l00095"></a>00095 
<a name="l00096"></a>00096                         <span class="keywordflow">if</span>(<a class="code" href="namespace_vtl_1_1geometry.html#a7b87e4beaa2a5ccef63a4b44d3e12e29" title="Checks if the vectors are almost parallel to each other.">geometry::vectorParallelTovector</a>(u,_Line.direction()))
<a name="l00097"></a>00097                                 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00098"></a>00098 
<a name="l00099"></a>00099                         Hyperplane plane(normal, _Face[0]);
<a name="l00100"></a>00100                         Scalar t = _Line.intersection(plane);
<a name="l00101"></a>00101                         VectorType point = _Line.origin() + _Line.direction() * t;
<a name="l00102"></a>00102 
<a name="l00103"></a>00103                         <span class="keywordflow">if</span>(powl(t,2) - _Line.direction().squaredNorm() &gt; _Eps)
<a name="l00104"></a>00104                                 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00105"></a>00105 
<a name="l00106"></a>00106                         <span class="keywordflow">if</span>(!<a class="code" href="namespace_vtl_1_1geometry.html#a88cd07d2a032075bcd62fbdaf57d3bb5" title="Checks if the given point is inside the Polygon face.">geometry::pointInPolygon</a>(point, _Face))
<a name="l00107"></a>00107                                 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00108"></a>00108 
<a name="l00109"></a>00109                         <span class="keywordflow">if</span>(_Point != NULL)
<a name="l00110"></a>00110                                 *_Point = point; 
<a name="l00111"></a>00111 
<a name="l00112"></a>00112                         <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l00113"></a>00113 
<a name="l00114"></a>00114 
<a name="l00115"></a>00115                 }
<a name="l00116"></a>00116 
<a name="l00117"></a>00117                 <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar, <span class="keywordtype">int</span> Dimension&gt;
<a name="l00118"></a><a class="code" href="namespace_vtl_1_1intersections.html#a053799f976f76b79c72d7cf1f09d91bc">00118</a>                 <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespace_vtl_1_1intersections.html#a053799f976f76b79c72d7cf1f09d91bc" title="Intersects a line with polygon in [i,j] plane.">lineWith2DPolygonIntersection</a>(<span class="keyword">const</span> Eigen::ParametrizedLine&lt;Scalar, Dimension&gt; &amp;_Line,
<a name="l00119"></a>00119                         <span class="keyword">const</span> <a class="code" href="class_vtl_1_1_polygon.html">Polygon&lt;Scalar, 2&gt;</a> &amp;_2DPolygon,
<a name="l00120"></a>00120                         std::vector&lt;Eigen::Matrix&lt;Scalar, 2, 1&gt;, Eigen::aligned_allocator&lt;Eigen::Matrix&lt;Scalar, 2, 1&gt;&gt;&gt; *_Points <span class="comment">/*= NULL*/</span>,
<a name="l00121"></a>00121                         <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;_Eps <span class="comment">/*= 1e-4*/</span>)
<a name="l00122"></a>00122                 {
<a name="l00123"></a>00123                         <span class="keyword">typedef</span> Eigen::Matrix&lt;Scalar, 2, 1&gt; VectorType;
<a name="l00124"></a>00124                         <span class="keyword">typedef</span> Eigen::ParametrizedLine&lt;Scalar, 2&gt; ParametrizedLine;
<a name="l00125"></a>00125                         <span class="keyword">typedef</span> std::map&lt;Scalar, VectorType, std::less&lt;Scalar&gt;, Eigen::aligned_allocator&lt;std::pair&lt;Scalar, VectorType&gt;&gt;&gt; IntersectionMap;
<a name="l00126"></a>00126                         <span class="keyword">typedef</span> IntersectionMap::value_type MapValueType;
<a name="l00127"></a>00127                         <span class="keyword">typedef</span> IntersectionMap::iterator IntersectionMapIterator;
<a name="l00128"></a>00128 
<a name="l00129"></a>00129                         ParametrizedLine line = <a class="code" href="namespace_vtl_1_1common.html#aba64bee77f1cd26116896d19ebed98e7" title="Converts the given vector to 2D [i,j] only.">common::convertTo2D</a>(_Line);
<a name="l00130"></a>00130                         <span class="keywordflow">if</span>(!_2DPolygon.<a class="code" href="class_vtl_1_1_polygon.html#aedf8c62294cb6547c81544b5139d604d" title="Returns the bounding box.">getBoundingBox</a>().IntersectWithLine(line))
<a name="l00131"></a>00131                                 <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00132"></a>00132 
<a name="l00133"></a>00133                         IntersectionMap intersections;
<a name="l00134"></a>00134 
<a name="l00135"></a>00135                         <span class="keywordflow">for</span> (<span class="keywordtype">int</span> a=0,b=1,num_ab = _2DPolygon.<a class="code" href="class_vtl_1_1_polygon.html#a365f08056e2072dde33bbfa552a5c505" title="Returns the vertex count in the array.">getVertexCount</a>();
<a name="l00136"></a>00136                                 a&lt;num_ab;++a,++b)
<a name="l00137"></a>00137                         {
<a name="l00138"></a>00138                                 ParametrizedLine edge;
<a name="l00139"></a>00139                                 <span class="keywordflow">if</span>(b&lt;num_ab)
<a name="l00140"></a>00140                                         edge = ParametrizedLine(_2DPolygon[a],_2DPolygon[b] - _2DPolygon[a]);
<a name="l00141"></a>00141                                 <span class="keywordflow">else</span>
<a name="l00142"></a>00142                                         edge = ParametrizedLine(_2DPolygon[a],_2DPolygon[0] - _2DPolygon[a]);
<a name="l00143"></a>00143 
<a name="l00144"></a>00144                                 VectorType point;
<a name="l00145"></a>00145                                 <span class="keywordflow">if</span>(<a class="code" href="namespace_vtl_1_1intersections.html#a98449060e8a8660d4a37a3623dfe8271" title="Intersects two lines(Rays).">lineWithLineIntersection</a>(line, edge, &amp;point, _Eps) &amp;&amp; 
<a name="l00146"></a>00146                                         <a class="code" href="namespace_vtl_1_1geometry.html#a7b062e373a0a37d6eabaa7e56c8e3a27" title="Checks if the given line segment (from start to end of line only) goes through the point...">geometry::pointOnLineSegment</a>(point, edge, _Eps))
<a name="l00147"></a>00147                                 {
<a name="l00148"></a>00148                                         <span class="keywordflow">if</span>(_Points==NULL)
<a name="l00149"></a>00149                                                 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l00150"></a>00150                                         intersections.insert(MapValueType(<a class="code" href="namespace_vtl_1_1common.html#a1efc29f177e2583d22a574d556919602" title="Returns the euclidean distance between two points.">distance</a>(line.origin(), point), point));
<a name="l00151"></a>00151                                 }
<a name="l00152"></a>00152 
<a name="l00153"></a>00153                         }
<a name="l00154"></a>00154                         <span class="keywordflow">if</span>(_Points!= NULL &amp;&amp;
<a name="l00155"></a>00155                                 intersections.size()&gt;0)
<a name="l00156"></a>00156                         {
<a name="l00157"></a>00157                                 <span class="keywordflow">for</span>(IntersectionMapIterator i = intersections.begin(),
<a name="l00158"></a>00158                                         end = intersections.end();
<a name="l00159"></a>00159                                         i!=end;i++)
<a name="l00160"></a>00160                                 {
<a name="l00161"></a>00161                                         _Points-&gt;push_back(i-&gt;second);
<a name="l00162"></a>00162                                 }
<a name="l00163"></a>00163                                 <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l00164"></a>00164                         }
<a name="l00165"></a>00165                         <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00166"></a>00166                 }
<a name="l00167"></a>00167 
<a name="l00168"></a>00168                 <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar, <span class="keywordtype">int</span> Dimension&gt;
<a name="l00169"></a><a class="code" href="namespace_vtl_1_1intersections.html#a2c41afd47e2b4a7815639e0d7374ba49">00169</a>                 <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="namespace_vtl_1_1intersections.html#a2c41afd47e2b4a7815639e0d7374ba49" title="Intersects a line with an excluded polygon.">lineWithExcludedPolygonIntersection</a>(<span class="keyword">const</span> Eigen::ParametrizedLine&lt;Scalar, Dimension&gt; &amp;_Line,
<a name="l00170"></a>00170                         <span class="keyword">const</span> <a class="code" href="class_vtl_1_1_polygon.html">Polygon&lt;Scalar, 2&gt;</a> &amp;_2DPolygon,
<a name="l00171"></a>00171                         <span class="keyword">const</span> Scalar &amp;_PolygonBaseLineHeight,
<a name="l00172"></a>00172                         <span class="keyword">const</span> Scalar &amp;_PolygonHeight,
<a name="l00173"></a>00173                         Eigen::Matrix&lt;Scalar, Dimension, 1&gt; *_Point <span class="comment">/*= NULL*/</span>,
<a name="l00174"></a>00174                         <span class="keyword">const</span> <span class="keywordtype">double</span> &amp;_Eps <span class="comment">/*= 1e-4*/</span>)
<a name="l00175"></a>00175                 {
<a name="l00176"></a>00176                         <span class="keyword">typedef</span> Eigen::Matrix&lt;Scalar, Dimension, 1&gt; VectorType;
<a name="l00177"></a>00177                         <span class="keyword">typedef</span> Eigen::Matrix&lt;Scalar, 2, 1&gt; VectorType2D;
<a name="l00178"></a>00178                         <span class="keyword">typedef</span> Eigen::ParametrizedLine&lt;Scalar, Dimension&gt; ParametrizedLine;
<a name="l00179"></a>00179                         <span class="keyword">typedef</span> Eigen::ParametrizedLine&lt;Scalar, 2&gt; ParametrizedLine2D;
<a name="l00180"></a>00180 
<a name="l00181"></a>00181                         std::vector&lt;VectorType2D, Eigen::aligned_allocator&lt;VectorType2D&gt;&gt; points;
<a name="l00182"></a>00182                         <span class="keywordflow">if</span>(<a class="code" href="namespace_vtl_1_1intersections.html#a053799f976f76b79c72d7cf1f09d91bc" title="Intersects a line with polygon in [i,j] plane.">lineWith2DPolygonIntersection</a>(_Line, _2DPolygon, &amp;points, _Eps))
<a name="l00183"></a>00183                         {
<a name="l00184"></a>00184                                 VectorType origin = <a class="code" href="namespace_vtl_1_1common.html#a098b2df81e6cc14cbf9697452e836f93" title="Converts the given vector to 3D using the given K value for [i,j, K].">common::convertTo3D</a>(points[0], _PolygonBaseLineHeight);
<a name="l00185"></a>00185                                 VectorType direction = <a class="code" href="namespace_vtl_1_1common.html#a098b2df81e6cc14cbf9697452e836f93" title="Converts the given vector to 3D using the given K value for [i,j, K].">common::convertTo3D</a>(points[0], _PolygonBaseLineHeight+_PolygonHeight) - origin;
<a name="l00186"></a>00186                                 ParametrizedLine vertical_line(origin, direction);
<a name="l00187"></a>00187                                 VectorType point;
<a name="l00188"></a>00188                                 <span class="keywordflow">if</span>(<a class="code" href="namespace_vtl_1_1intersections.html#a98449060e8a8660d4a37a3623dfe8271" title="Intersects two lines(Rays).">lineWithLineIntersection</a>(_Line, vertical_line, &amp;point, _Eps) &amp;&amp; 
<a name="l00189"></a>00189                                         <a class="code" href="namespace_vtl_1_1geometry.html#a7b062e373a0a37d6eabaa7e56c8e3a27" title="Checks if the given line segment (from start to end of line only) goes through the point...">geometry::pointOnLineSegment</a>(point, vertical_line, _Eps))
<a name="l00190"></a>00190                                 {
<a name="l00191"></a>00191                                         <span class="keywordflow">if</span>(_Point != NULL)
<a name="l00192"></a>00192                                                 *_Point = point;
<a name="l00193"></a>00193 
<a name="l00194"></a>00194                                         <span class="keywordflow">return</span> <span class="keyword">true</span>;
<a name="l00195"></a>00195                                 }
<a name="l00196"></a>00196                         }
<a name="l00197"></a>00197                         <span class="keywordflow">return</span> <span class="keyword">false</span>;
<a name="l00198"></a>00198                 }
<a name="l00199"></a>00199         };
<a name="l00200"></a>00200 };
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